Topological Levinson's theorem in presence of embedded thresholds and discontinuities of the scattering matrix,
with V. Austen D. Parra, A. Rennie, submitted.
Levinson's theorem for two-dimensional scattering systems: it was a surprise, it is now topological !,
with A. Alexander, D.T. Nguyen, A. Rennie, to appear in Journal of Spectral Theory.
Scattering theory and an index theorem on the radial part of SL(2,R),
with H. Inoue, to appear in Journal of Topology and Analysis.
Control Simulation Experiments of Extreme Events with the Lorenz-96 Model,
with Q. Sun, T. Miyoshi, Nonlin. Processes Geophys. 30 (2023), 117 - 128.
Analysis of COVID-19 in Japan with Extended SEIR model and ensemble Kalman filter,
with Q. Sun, T. Miyoshi, Journal of Computational and Applied Mathematics 419 (2023), 114772, 18 pages.
Analysis of COVID-19 spread in Tokyo through an agent-based model with data assimilation,
with C. Sun, T. Miyoshi, N. Tsuzu, J. Clin. Med. 11 (2022), 2401, 17 pages.
Decay estimates for unitary representations with applications to continuous- and discrete-time models,
with R. Tiedra de Aldecoa, Ann. Henri Poincaré 24 (2023), 1 - 36.
Spectral and scattering theory for topological crystals perturbed by infinitely many new edges,
with N. Tsuzu, Rev. Math. Phys. 34 (2022), 2250010, 26 pages.
Bibliometric analysis on mathematics, 3 snapshots: 2005, 2010, 2015,
with Q. Sun, Electron. J. App. Stat. Anal. 14 (2021), 90 - 116.
Scattering operator and wave operators for 2D Schroedinger operators with threshold obstructions,
with R. Tiedra de Aldecoa, L. Zhang, Complex Anal. Oper. Theory 15 (2021), article 106, 25 pages.
On radial Schroedinger operators with a Coulomb potential: General boundary conditions,
with J. Derezinski, J. Faupin, Q.N. Nguyen, Advances in Operator Theory 5 (2020), 1132 - 1192.
Discrete Laplacian in a half-space with a periodic surface potential I:
Resolvent expansions, scattering matrix, and wave operators,
with S. H. Nguyen, R. Tiedra de Aldecoa, Mathematische Nachrichten 295 (2022), 912 - 949.
Spectral and scattering theory of one-dimensional coupled photonic crystals,
with G. De Nittis, M. Moscolari, R. Tiedra de Aldecoa, Rev. Math. Phys. 33 (2021), 2150027, 40 pages.
Quantum walks with an anisotropic coin II: scattering theory,
with A. Suzuki and R. Tiedra de Aldecoa, Lett. Math. Phys. 109 (2019), 61 - 88.
On radial Schroedinger operators with a Coulomb potential,
with J. Derezinski, Ann. Henri Poincaré 19 (2018), 2869 - 2917.
Index theorems for Fredholm, semi-Fredholm, and almost periodic operators: all in one example,
with H. Inoue, J. Noncommut. Geom. 13 (2019), 1359 - 1380.
Quantum walks with an anisotropic coin I: spectral theory,
with A. Suzuki and R. Tiedra de Aldecoa, Lett. Math. Phys. 108 (2018), 331 - 357.
Does Levinson's theorem count complex eigenvalues ?
with F. Nicoleau and D. Parra, J. Math. Phys. 58 (2017), 102101-1 - 102101-7.
Spectral and scattering theory for Schroedinger operators on perturbed topological crystals,
with D. Parra, Rev. Math. Phys. 30 (2018), 1850009-1 - 1850009-39.
On Schroedinger operators with inverse square potentials on the half-line,
with J. Derezinski, Ann. Henri Poincaré 18 (2017), 869 - 928.
Commutator criteria for strong mixing II. More general and simpler,
with R. Tiedra de Aldecoa, CUBO 21 (2019), 37 - 48.
Continuity of the spectra for families of magnetic operators on Z^d,
with D. Parra, Anal. Math. Phys. 6 (2016), 327 - 343.
Schroedinger operators with n positive eigenvalues: an explicit construction involving complex valued potentials,
with J. Uchiyama and T. Umeda, Proc. Japan Acad. 92, Ser. A (2016), 7 - 12.
Spectral and scattering properties at thresholds for the Laplacian in a half-space
with a periodic boundary condition,
with R. Tiedra de Aldecoa, J. Math. Anal. Appl. 446 (2017), 1695 - 1722.
One-dimensional Dirac operators with zero-range interactions:
Spectral, scattering, and topological results,
with K. Pankrashkin, J. Math. Phys. 55 (2014), 062305-1 - 062305-17.
Resolvent expansions and continuity of the scattering matrix
at embedded thresholds: the case of quantum waveguides,
with R. Tiedra de Aldecoa, Bull. Soc. math. France 144 (2016), 251 - 277.
Explicit formulas for the Schroedinger wave operators in R^2,
with R. Tiedra de Aldecoa, C. R. Acad. Sci. Paris, Ser. I. 351 (2013), 209 - 214.
New expressions for the wave operators of Schroedinger operators in R^3,
with R. Tiedra de Aldecoa, Lett. Math. Phys. 103 (2013), 1207 - 1221.
Low energy spectral and scattering theory
for relativistic Schroedinger operators,
with T. Umeda, Hokkaido Mathematical Journal 45 (2016), 141 - 179.
Commutator methods for unitary operators,
with C. Fernandez and R. Tiedra de Aldecoa, J. Spectr. Theory 3 (2013), 271 - 292.
On the wave operators for the Friedrichs-Faddeev model,
with H. Isozaki, Ann. Henri Poincaré 13 (2012), 1469 - 1482.
Spectral analysis and time-dependent scattering theory
on manifolds with asymptotically cylindrical ends,
with R. Tiedra de Aldecoa, Rev. Math. Phys. 25 (2013), 1350003-1 - 1350003-40.
A few results on Mourre theory in a two-Hilbert spaces setting,
with R. Tiedra de Aldecoa, Anal. Math. Phys. 3 (2013), 183 - 200.
Levinson's theorem and higher degree traces for Aharonov-Bohm operators,
with J. Kellendonk and K. Pankrashkin, J. Math. Phys. 52 (2011), 052102-1 - 052102-28.
On the wave operators and Levinson's theorem
for potential scattering in R^3,
with J. Kellendonk, Asian-European Journal of Mathematics 5 (2012) 1250004-1 - 1250004-22.
Positive quantization in the presence of a variable magnetic field,
with M. Mantoiu and R. Purice, J. Math. Phys. 52 (2011), 112101-1 - 112101-15.
Time delay is a common feature of quantum scattering theory,
with R. Tiedra de Aldecoa, J. Math. Anal. Appl. 387 (2012), 618 - 630.
Spectral and scattering theory for the Aharonov-Bohm operators,
with K. Pankrashkin, Rev. Math. Phys. 23 (2011), 53 - 81.
Coherent states in the presence
of a variable magnetic field,
with M. Mantoiu and R. Purice, International Journal of Geometric Methods in Modern Physics 8 (2011), 187 - 202.
Magnetic pseudodifferential operators with coefficients in C*-algebras,
with M. Lein and M. Mantoiu, Publ. RIMS, Kyoto Univ. 46 (2010), 755 - 788.
New formulae for the wave operators for a rank one interaction,
with R. Tiedra de Aldecoa, Integral Equations and Operator Theory 66 (2010), 283 - 292.
The method of the weakly conjugate operator:
Extensions and applications to operators on graphs and groups,
with M. Mantoiu and R. Tiedra de Aldecoa, Petroleum - Gas University of Ploiesti Bulletin, Mathematics - informatics - physics Series LXI (2009), 1 - 12.
Weber-Schafheitlin type integrals with exponent 1,
with J. Kellendonk, Integral Transforms and Special Functions 20 (2009), 147 - 153.
On the structure of the wave operators in one dimensional
potential scattering,
with J. Kellendonk, Mathematical Physics Electronic Journal 14 (2008), 1 - 21.
The topological meaning of Levinson's theorem, half-bound states included,
with J. Kellendonk, J. Phys. A: Math. Theor. 41 (2008), 295207.
On
the spectrum of magnetic Dirac operators with Coulomb-type
perturbations,
with R. Tiedra de Aldecoa, J. Funct. Ana. 250 (2007), 625 - 641.
Spectral
analysis for adjacency operators on graphs,
with M. Mantoiu and R. Tiedra de Aldecoa, Ann. Henri Poincaré 8 (2007), 1401 - 1423.
Spectral
and propagation results for magnetic Schroedinger operators;
a C*-algebraic framework,
with M. Mantoiu and R. Purice, J. Funct. Ana. 250 (2007), 42 - 67.
On
the essential spectrum of magnetic pseudodifferential
operators,
with M. Mantoiu and R. Purice, C. R. Acad. Sci. Paris, Ser. I 344 (2007), 11 - 14.
Levinson's theorem for Schroedinger operators with point interaction: a
topological approach,
with J. Kellendonk, J. Phys. A: Math Gen. 39 (2006), 14397 - 14403.
Some
improvements in the method of the weakly conjugate
operator,
Letters in Mathematical Physics 76 (2006), 27 - 36.
Spectral
and scattering theory for Schroedinger operators with Cartesian
anisotropy,
Publ. RIMS, Kyoto Univ. 41 (2005), 73 - 111.
On
perturbations of Dirac operators with variable magnetic field of
constant direction,
with R. Tiedra de Aldecoa, J. Math. Phys. 45 (2004), 4164 - 4173.
Minimal
escape velocities for unitary evolution groups,
Ann. Henri Poincaré 5 (2004), 915 - 928.
Absence
of singular spectrum for Schroedinger operators with anisotropic
potentials and magnetic fields,
with M. Mantoiu, J. Math. Phys. 41 (2000), 2732 - 2740.
On some integral operators appearing in scattering theory,
and their resolutions,
with T. Umeda, in Spectral Theory and Mathematical Physics, 243 - 256, Latin American Mathematics Series, Springer, 2020.
Topological Levinson's theorem for inverse square potentials:
complex, infinite, but not exceptional,
with H. Inoue, Rev. Roumaine Math. Pures Appl. 64 (2&3), 225 - 250, 2019.
Levinson's theorem: an index theorem in scattering theory,
in Proceedings of the Conference Spectral Theory and Mathematical Physics, Santiago 2014, Operator Theory: Advances and Applications 254, 149 - 203, Birkhäuser, 2016.
A new formula relating localisation operators to time operators,
with R. Tiedra de Aldecoa, in Spectral Analysis of Quantum Hamiltonians, Operator Theory: Advances and Applications 224, 301 - 338, Birkhäuser/Springer, Basel, 2012.
New formulae for the Aharonov-Bohm wave operators,
Spectral and Scattering Theory for Quantum Magnetic Systems, 159 - 168, Contemporary Mathematics 500, AMS, Providence, Rhode Island, 2009.
Topological
boundary maps in physics: General theory and
applications,with J. Kellendonk, Perspectives in Operator Algebras and Mathematical Physics, 105 - 121, Theta, Bucharest, 2008.
Twisted
crossed products and magnetic pseudodifferential
operators,
with M. Mantoiu and R. Purice, Advances in Operator Algebras and Mathematical Physics, 137 - 172, Theta Ser. Adv. Math. 5, Theta, Bucharest, 2005.
Discrete Laplacian in a half-space with a periodic surface potential: an overview of analytical investigations,
RIMS Kokyuroku 2195, 18 - 26, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 2021.
Periodic Schroedinger operators on topological crystals:
framework, analytically fibered operator, conjugate operator,
RIMS Kokyuroku 2123, 51 - 68, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 2019.
Inner and outer continuity of the spectra for families of magnetic operators on Z^d,
RIMS Kokyuroku 2023, 69 - 76, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 2017.
Time delay for an abstract quantum scattering process,
RIMS Kokyuroku 1760, 33 - 43, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 2011.
A few results in scattering theory: Time operator, time delay, Mourre theory and topological Levinson's theorems,
HDR Thesis (2011), University of Lyon.
Commutator
methods in spectral and scattering theory,
(partially in French), PhD Thesis (2004), University of Geneva.
Analyse
spectrale d'hamiltoniens à champ magnétique pour des systèmes
bidimensionnels,
(French), Diploma Thesis (1999), University of Lausanne.